We have calculated, from X-ray diffraction data, the electron density maps of the ripple phase of dimyristoylphosphatidylcholine (DMPC) and palmitoyl-oleoyl phosphatidylcholine (POPC) multibilayers at different temperatures and fixed relative humidity. Our analysis of the maps establishes the existence of an average tilt of the hydrocarbon chains of the lipid molecules along the direction of the ripple wave vector, which we believe is responsible for the occurrence of asymmetric ripples in these systems.